# Inflow Prediction of Centralized Reservoir for the Operation of Pump Station in Urban Drainage Systems Using Improved Multilayer Perceptron Using Existing Optimizers Combined with Metaheuristic Optimization Algorithms

## Abstract

**:**

## 1. Introduction

## 2. Methodologies

#### 2.1. Overview

#### 2.2. Preparation of Training Data

#### 2.2.1. Correlation Analysis

_{x,y}is the correlation coefficient, x

_{i}is the input data, y

_{i}is the target data, $\overline{x}$ is the average of x

_{i}, and $\overline{y}$ is the average of y

_{i}. Figure 2 shows the application of a correlation analysis considering the lag time.

#### 2.2.2. Normalization of Training Data

_{i}is the normalized value, x

_{i}is the observed value, x

_{b}and x

_{a}are the maximum and minimum observed values, respectively.

#### 2.3. MLP Combined with IHS

#### 2.3.1. Existing Optimizers in MLP

#### 2.3.2. IHS

_{min}and PAR

_{max}are the lower and upper boundaries of PAR, respectively; I

_{c}is the number of current iterations; and I

_{t}is the total number of iterations. BW, which is the range of a local search in HS, affects the results. Equation (4) shows the expression of BW in IHS:

_{min}and BW

_{max}are the lower and upper boundaries of BW, respectively. The IHS procedure is as follows:

- Step 1. Create initial solutions based on the range of decision variables and generate the HMS.
- Step 2. Sort the HM in HMS based on the value of the objective function.
- Step 3(a). Select decision variables in the existing HM when HMCR is applied.
- Step 3(b). Adjust new decision variables based on BW when PAR is applied.
- Step 4. Create a new solution using the decision variables created in Steps 3(a) and 3(b).
- Step 5. Compare the new solution with the worst solution in the existing HM to decide whether it should be replaced.
- Step 6. Repeat Steps 2 to 5 until the termination criteria is satisfied.

_{max}; 0.1, for PAR

_{min}; 0.01, for BW

_{max}; and 0.001, for BW

_{min}.

#### 2.3.3. Combined Optimizer Using Metaheuristic Optimization in MLP

#### 2.4. Selection of Monitoring Nodes

#### 2.4.1. Selection of Maximum Flooding Nodes

#### 2.4.2. Selection of First Flooding Nodes

^{2}, it is classified as a main conduit; otherwise, it is classified as a branch conduit [25]. For the applied duration, the concentration time within the study area was applied up to three times.

## 3. Application and Results

#### 3.1. Study Area

^{2}. Eleven pump stations are installed at the Dorim Stream, and the Daerim3 pump station has the largest drainage area. The Daerim3 pump station comprises 12 pumps (with a drainage capacity of 57.02 m

^{3}/s) and has a drainage area of 2.49 km

^{2}. The Daerim3 pump station has a CR that can receive inflow from the drainage area, the capacity of which is 36,200 m

^{3}. In the network shown on the right side of Figure 5, the CR is located downstream of the drainage area. Additionally, the first and maximum flooding nodes selected in this study are indicated.

#### 3.2. Preparation of Data for Inflow Prediction of CR

#### 3.3. Inflow Prediction Using MLPIHS

_{o}is the observed data, x

_{i}is the simulated data, and n is the number of data points. The MAE is expressed as shown in Equation (6):

_{o}is the observed data, x

_{i}is the simulated data, and n is the number of data points. Table 5 shows the results of the inflow prediction.

## 4. Discussion

^{2}values for the observed and predicted inflows for each MLP were calculated. The value of R

^{2}is expressed as shown in Equation (7):

_{o}is the observed data, x

_{i}is the simulated data, n is the number of data points, and $\overline{x}$ is the average of x

_{o}. Additionally, a comparison was conducted based on the flow rates of the observed and predicted inflows. Figure 8 shows a comparison of R

^{2}for the observed and predicted inflows when using Adam.

^{2}for the observed and predicted inflows when using Ftrl+HS.

^{2}for the observed and predicted inflows using Ftrl+IHS.

## 5. Conclusions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

CR | Centralized reservoir |

DR | Decentralized reservoir |

UDS | Urban drainage system |

MLP | Multilayer perceptron |

ANN | Artificial neural network |

RNN | Recurrent neural network |

CNN | Convolutional neural network |

LSTM | Long short-term memory |

GRU | Gated recurrent unit |

GA | Genetic algorithm |

PSO | Particle swarm optimization |

HS | Harmony search |

IHS | Improved harmony search |

RCGA | Real-coded genetic algorithm |

MLPHS | MLP using new optimizer combined with HS |

MLPIHS | MLP using new optimizer combined with IHS |

GD | Gradient descent |

SGD | Stochastic gradient descent |

NAG | Nesterov accelerated gradient |

Adagrad | Adaptive gradient |

RMSprop | Root mean squared propagation |

AdaDelta | Adaptive delta |

Adam | Adaptive moment |

Nadam | Nesterov accelerated adaptive moment |

HMS | Harmony memory size |

HMCR | Harmony memory considering rate |

PAR | Pitch adjusting rate |

BW | Bandwidth |

HM | Harmony memory |

SWMM | Storm water management model |

MSE | Mean square error |

MAE | Mean absolute error |

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Optimizers | Description |
---|---|

Adadelta | Update the learning rate using a Hessian matrix and exponential average |

Adagrad | Use a flexible learning rate based on the learning process |

Adam | Combine momentum and RMSporp |

Adamax | Apply a new infinity norm |

Ftrl | Normalize the follow the leader by considering gradient (leader) with the smallest loss |

Nadam | Combine Nesterov accelerated gradient and RMSprop |

RMSprop | Improve learning stopping using an exponential average |

SGD | Select randomly from the entire data set |

Rainfall Events | 2010 | 2011 | 2012 | 2013 | 2014 | 2016 | 2018 | 2019 |
---|---|---|---|---|---|---|---|---|

Maximum flooding nodes | 550 | 550 | 550 | 550 | 550 | 550 | 550 | 550 |

Duration (m) | 30 | 60 | 90 |
---|---|---|---|

First flooding nodes | 560 | 560 | 575 |

Data Type | Monitoring Node (550) | Monitoring Node (560) | Monitoring Node (575) | Rainfall Data |
---|---|---|---|---|

Lag time (min) | 15 | 14 | 13 | 17 |

Correlation coefficient | 0.813 | 0.949 | 0.952 | 0.747 |

Method | Adadelta | Adagrad | Adam | Adamax | Ftrl | Nadam | RMSprop | SGD |
---|---|---|---|---|---|---|---|---|

MSE | 4.312000 | 5.970060 | 3.082933 | 3.106901 | 11.978707 | 3.199255 | 3.261781 | 6.689764 |

MAE | 1.285771 | 1.261158 | 1.021378 | 1.024476 | 1.635111 | 1.036619 | 1.085643 | 1.443204 |

Method | Adadelta+HS | Adagrad+HS | Adam+HS | Adamax+HS | Ftrl+HS | Nadam+HS | RMSprop+HS | SGD+HS |

MSE | 3.199255 | 3.088522 | 3.071538 | 3.078417 | 2.936929 | 3.137013 | 3.034306 | 4.901860 |

MAE | 1.036619 | 1.028809 | 1.018922 | 1.025179 | 1.001793 | 1.044988 | 1.015344 | 1.304466 |

Method | Adadelta+IHS | Adagrad+IHS | Adam+IHS | Adamax+IHS | Ftrl+IHS | Nadam+IHS | RMSprop+IHS | SGD+IHS |

MSE | 3.029370 | 2.984212 | 3.047000 | 3.046682 | 2.930192 | 3.119831 | 3.020394 | 3.247332 |

MAE | 1.017907 | 1.020483 | 1.030821 | 1.024705 | 0.989532 | 1.037507 | 1.000169 | 1.177632 |

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**MDPI and ACS Style**

Lee, E.H.
Inflow Prediction of Centralized Reservoir for the Operation of Pump Station in Urban Drainage Systems Using Improved Multilayer Perceptron Using Existing Optimizers Combined with Metaheuristic Optimization Algorithms. *Water* **2023**, *15*, 1543.
https://doi.org/10.3390/w15081543

**AMA Style**

Lee EH.
Inflow Prediction of Centralized Reservoir for the Operation of Pump Station in Urban Drainage Systems Using Improved Multilayer Perceptron Using Existing Optimizers Combined with Metaheuristic Optimization Algorithms. *Water*. 2023; 15(8):1543.
https://doi.org/10.3390/w15081543

**Chicago/Turabian Style**

Lee, Eui Hoon.
2023. "Inflow Prediction of Centralized Reservoir for the Operation of Pump Station in Urban Drainage Systems Using Improved Multilayer Perceptron Using Existing Optimizers Combined with Metaheuristic Optimization Algorithms" *Water* 15, no. 8: 1543.
https://doi.org/10.3390/w15081543